This group attempted to register the trademark by extension to the USPTO and was denied for several reasons. Reason #2 for the denial was "Likelihood of Confusion" and points at the existing PostgreSQL trademark on file.

https://www3.wipo.int/madrid/monitor/en/showData.jsp?ID=ROM.... -> Real-time Status and then -> Documents -> United States of America -> (PDF link) https://madrid.wipo.int/documentaccess/documentAccess?docid=...